Presets
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Wind, pump and rain
Rotor power is 1/2 rho pi R2 Cp v3. The pump moves the smaller of what the wheel displaces and what the wind energy can lift through the head.
Yaw
Model checks
The science
What is modelled
A windpump rotor feeding a scoop wheel. Wind power is reduced by the cosine of the yaw error to the third power; flow is capped both by wheel displacement and by pump energy, and a storage basin gains rain runoff and loses pumped water.
Equations
- Rotor power
P = 1/2 rho pi R2 Cp (v cos d)3, shaft powerP x eta_drive x (1 - brake). - Energy-limited flow
q = eta_pump P / (rho_w g H); displacement flowrpm x ratio x volume per turn. - Storage
A dh/dt = q_in - q_out.
Checks run in the page
- Rotor power from the formula.
- cos3 yaw loss at 60 degrees.
- Pump flow equal to the smaller of the two limits.
- Water balance of rain, pumping and level change.
Honest simplifications
A demonstration-scale energy model: constant power coefficient, first-order rotor speed response, no tip-speed-ratio curve, no frictional losses beyond fixed efficiencies and rain treated as uniform runoff. Not a drainage design tool.
What to try
- Press Cap misaligned (and untick automatic yaw) to see the cos3 loss.
- Press Storm, braked: the brake limits the power in strong wind.
- Press Light air, high lift to see the energy-limited regime.